Question:-  May stakes defining a water hazard or lateral water hazard be moved?

Answer:- YES

A water hazard stake is an obstruction - see Definition of "Obstruction".

Consequently, if such a stake is moveable, it may be removed, without penalty, in accordance with Rule 24-1.

A player may remove a movable obstruction anywhere on the course, irrespective of whether the ball lies in a hazard or not.

Question:-

May a stake defining Out of Bounds be moved?

Answer: - No

Under Definition of "Obstruction" an object (i.e. a stake) defining out of bounds is not an obstruction therefore you can not obtain relief.